Let us specify the discrete choice demand in detail. For our model, we concentrate on random utility errors which follow the nested logit distribution from [1]} given by the probability density function
\(f_\epsilon \left(z\right) = \exp \left(-\sum \limits _{\ell =1}^{L} \left(\sum \limits _{i \in N_\ell }^{} e^{-z^{(i)} /\mu _\ell }\right)^{\mu _\ell }\right),\) 
